Can Vimeo tell me if my video counts as fair use?

No. We would if we could, but there is no way to easily answer that question. Each Vimeo member is solely responsible for making sure their videos don’t infringe on the copyrights of others. You can upload videos with material that you consider to be fair use, but you do so at your own risk.

That means you should think through the four factors of fair use and see if you can apply them to your videos.